Papers
This section presents a collection of AHP/ANP papers. Whether you are a student, academic and/or professional in the field of decision making, you can help us expand this collection by sharing your papers on decision making with the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP).
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Paper results for keyword: Graph theoryOperations Research: Some Contributions to Mathematics: Applied mathematics gets a new surge of life from techniques of operations research
Thomas SaatyJournal: ScienceThe discussion of fuzzy sets indicates that set theory should be extended to make it more suitable for the development of algebraic structures with wider applications. Stochastic optimization, a synthesis of the three areas of continuum mathematics, is a rapidly growing field particularly in the ...
Read MoreThirteen colorful variations on Guthrie
Thomas SaatyJournal: The American Mathematical MonthlyAfter careful analysis of information regarding the origins of the four-color conjecture, Kenneth O. May concludes that:
It was not the culmination of a series of individual efforts that flashes across the mind of Francis Guthrie while coloring a map of England... his brother communicated the co...
Read MoreThe minimum number of intersections in complete graphs
Thomas SaatyJournal: Proceedings of the National Academy of Sciences of the United States of AmericaZarankiewicz has developed results concerning the minimum number of edge intersections, when drawn in a plane, of the bipartite graph consisting of two sets of vertices with one edge joining each element of one set to each element of the other set. When each set has three vertices, we have one of...
Read MoreRemarks on the four color problem; the Kempe catastrophe
Thomas SaatyJournal: Mathematics MagazineThe original error discovered by Heawood in Kempe's attempt to prove the four-color conjecture is often encountered by many of those who follow the inductive argument approach to the problem. Perhaps the nature of the difficulty is not well appreciated. An old Chinese proverb urges that to know t...
Read MoreOn polynomials and crossing numbers of complete graphs
Thomas SaatyJournal: Journal of Combinatorial TheoryA long-standing, unsolved problem is that of finding the minimum number of crossings of the edges in a complete graph when embedded on a surface of genus zero.
Read More
Operations Research: Some Contributions to Mathematics: Applied mathematics gets a new surge of life from techniques of operations research
Thomas SaatyJournal: ScienceThe discussion of fuzzy sets indicates that set theory should be extended to make it more suitable for the development of algebraic structures with wider applications. Stochastic optimization, a synthesis of the three areas of continuum mathematics, is a rapidly growing field particularly in the ...
Read MoreThirteen colorful variations on Guthrie
Thomas SaatyJournal: The American Mathematical MonthlyAfter careful analysis of information regarding the origins of the four-color conjecture, Kenneth O. May concludes that: It was not the culmination of a series of individual efforts that flashes across the mind of Francis Guthrie while coloring a map of England... his brother communicated the co...
Read MoreThe minimum number of intersections in complete graphs
Thomas SaatyJournal: Proceedings of the National Academy of Sciences of the United States of AmericaZarankiewicz has developed results concerning the minimum number of edge intersections, when drawn in a plane, of the bipartite graph consisting of two sets of vertices with one edge joining each element of one set to each element of the other set. When each set has three vertices, we have one of...
Read MoreRemarks on the four color problem; the Kempe catastrophe
Thomas SaatyJournal: Mathematics MagazineThe original error discovered by Heawood in Kempe's attempt to prove the four-color conjecture is often encountered by many of those who follow the inductive argument approach to the problem. Perhaps the nature of the difficulty is not well appreciated. An old Chinese proverb urges that to know t...
Read MoreOn polynomials and crossing numbers of complete graphs
Thomas SaatyJournal: Journal of Combinatorial TheoryA long-standing, unsolved problem is that of finding the minimum number of crossings of the edges in a complete graph when embedded on a surface of genus zero.
Read More